The files found on this site are .mod, .s3m and .it. They can be played with media players like winamp. But for better results, there exist other track players like XMPlayer and ModPlug Player; to name some.
Or you can use the very same tracker (which is the editing program). I recommend Schism Tracker or Impulse Tracker (for win 98) to play .s3m and .it files. The original tracker of the file will render the most faithful playback.
You can find many others here.